Why does length contraction happen only in the direction of motion?

Length contraction happens only in direction of motion. Never perpendicular to the motion.
My questions are
1) Why is it so?. For an observer in the same frame, it would mean a meter scale to give 2 different results. If by some means he is able to calculate the difference won't he be able to tell that he is in motion, thus violating POR?
2) What happens to the lengths neither perpendicular, nor parallel to the direction of motion?. Is the contraction according to trigonometry?

For the observer "in the same frame" there is no perception of length contraction and he would see the stick appear the same no matter what way he oriented. It's the same as with time dilation. It is an artifact of different reference frames, not something perceived by the person IN the fast-moving reference frame.

For the observer "in the same frame" there is no perception of length contraction and he would see the stick appear the same no matter what way he oriented. It's the same as with time dilation. It is an artifact of different reference frames, not something perceived by the person IN the fast-moving reference frame.

But where it gets really tricky is when you try to convert this to general relativity. Is there length contraction in a gravitational field, as there would be in an accelerating reference frame? And, in that case, is the length contraction only in one direction?

But where it gets really tricky is when you try to convert this to general relativity. Is there length contraction in a gravitational field, as there would be in an accelerating reference frame? And, in that case, is the length contraction only in one direction?

The length contraction is an artifact of different reference frames and yes, it occurs in one direction only (parallel to the lines of gravitational force). If I understand it correctly, the length contraction in a gravitational field is due to the fact that the light from the farther end of the meter stick is slowed down (red shifted) more by the tidal effect than is the light from the nearer end and this is what gives rise the perceptions of time dilation and length contraction.

Hm ... rereading what I just wrote, I see that it would seem (I think) that the different red shifts would cause the meter stick to look LONGER not shorter.

@ phinds
yes agreed. But isn't time dilation a direct consequence of constant speed of light?. If light behaved the same way as a ball, then the speed of light in a moving frame would be different for different frames. If my frame of reference was at rest and if it started moving(consider i know it), then having a constant light speed, I can discern that time and space are no more the same for me as they were earlier. The fact that I know that my frame has a different speed, yet I have the same speed of light relative to me, makes me aware that perception of space and time have changed for me. Thus can I infer that length contraction has happened only in direction parallel to the motion, and not in perpendicular direction?. Wouldn't I get different results?

@ phinds
yes agreed. But isn't time dilation a direct consequence of constant speed of light?. If light behaved the same way as a ball, then the speed of light in a moving frame would be different for different frames. If my frame of reference was at rest and if it started moving(consider i know it), then having a constant light speed, I can discern that time and space are no more the same for me as they were earlier. The fact that I know that my frame has a different speed, yet I have the same speed of light relative to me, makes me aware that perception of space and time have changed for me. Thus can I infer that length contraction has happened only in direction parallel to the motion, and not in perpendicular direction?. Wouldn't I get different results?

Well, I don't like to think of it as a CONSEQUENCE of light but rather a consequence of the fact that there is a universal speed limit towards which velocities can approach asymptotically but never reach. THAT is the reason for the effects. LIGHT is just a convenient way to DEMONSTRATE it (because light goes at the universal speed lmiit and it's something we can reference as SEEING rather than just imagining).

Yes, length contraction and time dilation only occur in the direction of motion. That is, in whatever coordinate system you use to descibe the moving object, you can create a vector sum that is THE direction of motion and that's the direction along which those things happen.